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Prove that |veca xx vecb|^(2) = abs(veca...

Prove that `|veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)`

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Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

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Prove that : |veca + vecb|le|veca|+|vecb| .

What is abs(veca-vecb)=if abs(veca)=3,abs(vecb)=4 and abs(veca+vecb)=5 ?

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

|veca| = |vecb| = veca = vecb .

Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

What is the angle between veca and vecb if abs(veca+vecb)=abs(veca-vecb) ?

Prove that two vactors are perpendicular iff |veca+vecb|^2 = |veca|^2 + |vecb|^2

For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk , obtain vecaxx(vecbxxvecc) and also verify the formula vecaxx(vecbxxvecc) = (veca.vecc)vecb-(veca.vecb)vecc .

ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section B
  1. The plane lx+my=0 is rotated about its line of intersection with the p...

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  2. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin an...

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  3. Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * v...

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  4. Find the vector equation of a plane which is at a distance of 6 units ...

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  5. If sin{cot^(-1)(x + 1)} = cos(tan^(-1)x), then find x.

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  6. One kind of cake requires 200 g of flour and 25 g of fat and another k...

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  7. Consider f:R(+) to [-5, oo) given by f(x)=9x^(2)+6x-5. Show that f i...

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  8. Let R be a relation on the set A of ordered pairs of positive integers...

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  9. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  10. Two persons A and B throw a die alternately till one of them gets a th...

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  11. A = [(1, 0), (0, 1)], B = [(1, 0), (0, -1)] and C = [(0, 1), (1, 0)], ...

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  12. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  13. An urn contains 4 white and 6 red balls. Four balls are drawn at rando...

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  14. Using differentials, find approximate value (3.968)^(3//2)

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  15. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

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  16. If xy log(x + y) = 1, then prove that (dy)/(dx) = -(y(x^(2)y + x +...

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  17. If sin 2x = (2t)/(1 + t^(2)), tan y = (2t)/(1 - t^(2)) then find (dy)/...

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  18. Using mean value theorem, prove that sin xltx,in(0.pi//2).

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  19. Solve (dy)/(dx)+y=cos x-sin x

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  20. Find the equation of the curve passing through the point (1, 1) whose ...

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